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Edge-based a Posteriori Error Estimators for GeneratingQuasi-optimal Simplicial Meshes

Published online by Cambridge University Press:  26 August 2010

A. Taik ,
A. Agouzal ,
K. Lipnikov  and
Yu. Vassilevsk
A. Agouzal
Affiliation:
University Lyon1, Institute Camille Jordan, UMR 5208, 69100 Villeurbanne, France
K. Lipnikov
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM, 87545, U.S.A.
Yu. Vassilevsk*
Affiliation:
Institute of Numerical Mathematics, Gubkina str. 8, Moscow 119333, Russia
*
* Corresponding author: E-mail:yuri.vassilevski@gmail.com
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Abstract

We present a new method for generating a d-dimensional simplicial meshthat minimizes the L p -norm,p > 0, of the interpolation error or its gradient. The methoduses edge-based error estimates to build a tensor metric. We describe and analyze thebasic steps of our method

Keywords

finite elementsanisotropic meshesa posteriori error estimates

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References

A. Agouzal, K. Lipnikov, Y. Vassilevski. Generation of quasi-optimal meshes based on a posteriori error estimates. In: Proceedings of 16th International Meshing Roundtable. M.Brewer and D.Marcum (eds.), Springer, (2007), 139–148.
A. Agouzal, K. Lipnikov, Y. Vassilevski. Hessian-free metric-based mesh adaptation via geometry of interpolation error. To appear in Comp. Math. Math. Phys., 50 (2010).
Vassilevski, Y., Lipnikov, K.. Adaptive algorithm for generation of quasi-optimal meshes . Comp. Math. Math. Phys., 39 (1999), 1532–1551.Google Scholar
Vassilevski, Y., Agouzal, A.. An unified asymptotic analysis of interpolation errors for optimal meshes . Doklady Mathematics, 72 (2005), 879–882.Google Scholar